【作者】 王辉；

【导师】 曹树刚；

【作者基本信息】 重庆大学 ， 矿业工程， 2022， 博士

【摘要】 受层理结构的影响,页岩在力学上会表现出明显的各向异性特征。在分析其在荷载作用下的力学响应时,通常可以将其简化为横观各向同性介质。而分析页岩的这种横观各向同性特征对其损伤和断裂性质的影响,并建立起能反映其横观各向同性性质的本构模型和断裂准则,对于指导页岩气开采具有重要的理论意义和工程实践价值。为此,本文以龙马溪组层状页岩为研究对象,采用室内试验和数值模拟相结合的方法对页岩的物理和力学各向异性特征进行了系统分析;同时,基于横观各向同性介质弹性理论,对页岩本构模型的建立、应力强度因子的求解以及断裂机理的分析进行了深入的研究。主要研究内容和成果如下:(1)对具有不同层理倾角的页岩进行了单轴、三轴压缩试验以及巴西劈裂试验,分别从破坏模式、强度特征、能量演化、特征应力和特征应变阈值以及破坏包络线在π平面上的分布规律等方面系统分析了页岩的力学各向异性特征;同时,结合微细观结构和纵波波速分布特征的分析结果,揭示了页岩力学性质表现出各向异性特征的内在机理。(2)根据单轴压缩试验和巴西劈裂试验结果分别计算得到了页岩的横观各向同性弹性参数以及视弹性模量和视泊松比,并验证了利用横观各向同性本构模型描述页岩弹性变形特征的合理性;在此基础上,通过引入修正的三维横观各向同性H-B准则和Weibull概率密度函数,建立了页岩的横观各向同性统计损伤本构模型,并利用单轴和三轴试验对模型进行了验证,同时探讨了模型参数的物理意义。(3)基于颗粒流离散元理论,借助颗粒流程序PFC3D建立了页岩的数值计算模型,开展了三轴压缩条件下页岩各向异性力学特征的模拟研究;从微裂纹演化、接触力链分布以及颗粒位移变化等角度分析了页岩的细观力学特征,同时从细观角度揭示了页岩在变形破坏过程中的损伤演化机制,并探讨了页岩细观参数对其宏观力学特征的影响。(4)利用复变函数法并结合边界条件的傅里叶展开级数,推导了在具有不同分布形式边界载荷作用下的横观各向同性圆盘的应力解析解,得到了应力集中因子的求解公式,同时分析了解的收敛性特征以及弹性参数对应力集中因子的影响。在此基础上,提出了一种基于含中心直裂纹巴西圆盘(CSTBD)结构的裂纹应力强度因子的权函数求解方法,并利用已有的求解数据对该方法的可行性进行了验证。(5)利用CSTBD试件对页岩进行了不同加载模式下的断裂力学试验,分析了试件的破坏强度、裂纹扩展形态、破坏模式以及声发射时间分布特征;同时,基于测试结果,分别利用横观各向同性介质中求解裂纹应力强度因子的有限元法和权函数法计算得到了页岩的断裂韧度,分析了页岩断裂韧度的各向异性特征,并得到了断裂韧度与裂纹倾角以及层理倾角的多项式函数关系表达式。(6)基于横观各向同性介质断裂力学理论,并考虑裂纹尖端T应力和塑性区的影响,通过引入横观各向同性介质的最大拉应力准则,建立了修正的横观各向同性介质的最大切向应力断裂准则,并利用页岩的断裂力学试验结果对该断裂准则的适用性进行了验证。更多还原

【Abstract】 Under the influence of bedding structure,shale exhibit obvious anisotropic characteristics in mechanics.The shale can be simplified as a transversely isotropic medium when analyzing its mechanical response under load.It is of important theoretical significance and engineering practical value for guiding shale gas production that analyzing the influence of the transverse isotropy of shale on its damage and fracture properties,and establishing the constitutive model and fracture criterion that can reflect the transverse isotropy of shale.In this paper,the physical and mechanical anisotropy characteristics of Longmaxi stratified shale are systematically analyzed by laboratory experiment and numerical simulation.At the same time,based on the elastic theory of transversely isotropic medium,the establishment of constitutive model,the solution of stress intensity factor and the analysis of fracture mechanism of shale are deeply studied.The main content and results of the paper are as follows:(1)Uniaxial compression tests,conventional triaxial compression tests,and Brazilian splitting tests were conducted on shale specimens with different bedding inclinations.The mechanical anisotropy characteristics of shale were systematically analyzed from the failure modes,strength characteristics,energy evolution,threshold values of characteristic stress and strain,and distribution rule of failure envelopes inπ-plane.At the same time,the internal mechanism of mechanical anisotropy of shale was revealed by combining the analysis results of micro-structure and P-wave velocity distribution.(2)According to the results of uniaxial compression test and Brazilian splitting test,the transverse isotropic elastic parameters,apparent elastic modulus and apparent Poisson’s ratio of shale were calculated,and the rationality of using the transverse isotropic constitutive model to describe the elastic deformation characteristics of shale was verified.Furthermore,a transversely isotropic statistical damage constitutive model of shale was established by introducing a modified three-dimensional transversely isotropic H-B criterion and Weibull probability density function,and the model was verified by uniaxial and triaxial tests,as well as the physical significance of model parameters was discussed.(3)Based on the discrete element theory of the particle flow,the numerical model of shale specimen was established by the Particle Flow Code in three-dimensions(PFC3D),and the simulation research on the anisotropic mechanical characteristics of shale under triaxial compression was carried out.Then,the meso-mechanical characteristics of shale were analyzed from the perspectives of microcrack evolution,force chain distribution of contact and particle displacement evolution.Meanwhile,the damage evolution mechanism of shale in the process of deformation and failure was revealed on the microscopic level,and the influence of meso-parameters on the macro-mechanical characteristics of shale was discussed.(4)Utilizing the complex variable function method and combined with the Fourier expansion series of boundary conditions,the analytical solution of the stress of a transversely isotropic disk under boundary load with different distribution forms was derived,as well as the solution formula of the stress concentration factors.Moreover,the convergence performance of the solution and the influence of elastic parameters on the stress concentration factors were analyzed.Then,a weight function method for solving the crack stress intensity factor based on the cracked straight-through Brazilian disc(CSTBD)structure was proposed,and the feasibility of the method was verified by using the existing solution data.(5)Fracture mechanics tests on shale under different loading modes were carried out with CSTBD specimens.The failure strength,crack propagation morphology,failure mode and temporal distribution characteristics of acoustic emission of the specimens were analyzed.Furthermore,based on the test results,the fracture toughness of shale was calculated by using the finite element method and weight function method to solve the crack stress intensity factor in transversely isotropic medium.The anisotropic characteristics of fracture toughness of shale were analyzed,and the polynomial function between the fracture toughness and crack inclination angle was obtained,as well as the polynomial function between the fracture toughness and bedding inclination angle.(6)Based on the fracture mechanics theory of transversely isotropic medium,and considering the influence of T-stress and plastic zone at the crack tip,the modified maximum tangential stress fracture criterion of transversely isotropic medium.At the same time,the applicability of the fracture criterion was verified by the results of fracture mechanics tests of shale.更多还原